Determining the Contribution of Spatial Sub-Regions to Structure Functions

A novel algorithm is presented for determining the structure function of a discretized heat diffusion problem. In this approach the thermal capacitances and thermal resistances defining the structure function are computed as weighted spatial averages of the volumetric heat capacity and thermal resistivity respectively. This information is able to reveal the physical meaning of structure function in 3-D heat diffusion problems. Also it can be exploited, for determining the exact contribution of the thermal resistivity and volumetric heat capacity in any sub-region of the spatial region in which the 3-D heat diffusion problem is defined, to each resistance and capacitance of the structure function.